Why can I pose my rigify model in Weight Paint mode, but not in Pose mode?
The issue seems to be the boolean modifier, which cuts your mesh with the nail mesh. when you disable the visibility of that modifier, the armature deforms the mesh as normal. I'm not 100% sure why this happens, if it is an issue due to laggy update because the boolean takes too long, or if the boolean (more likely) messes up your vertex groups, and thus the weights. It's also interesting that weight paint ignores the boolean apparently.